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15. A tuxedo rental company charges a flat fee of $200 plus a $50 per day fee to rent one of their tuxedos. The function that models the cost to rent a tuxedo is t(d)=50d+200, where d represents the number of days in which the tuxedo is rented and t represents the total cost of the rental.

Select all reasonable scales for the vertical axis.(3 points)
$1
$1

$5
$5

$25
$25

$50
$50

$100
$100

$400

3 answers

To determine reasonable scales for the vertical axis (cost) of the function \( t(d) = 50d + 200 \), we can analyze the function based on the values of \( d \) (the number of days).

  1. Minimum Cost: When \( d = 0 \): \[ t(0) = 50(0) + 200 = 200 \] The minimum cost is $200.

  2. For various values of \( d \):

    • \( d = 1 \): \( t(1) = 50(1) + 200 = 250 \)
    • \( d = 2 \): \( t(2) = 50(2) + 200 = 300 \)
    • \( d = 3 \): \( t(3) = 50(3) + 200 = 350 \)
    • \( d = 4 \): \( t(4) = 50(4) + 200 = 400 \)
    • And so on...

Given the range of values (starting from $200 and increasing), the reasonable scales for the vertical axis (the cost) would be those that make sense within this context and that can fit above $200.

Let's evaluate the options:

  • $1: Not reasonable, since the minimum cost is $200.
  • $5: Not reasonable, since the minimum cost is $200.
  • $25: Not reasonable, since the minimum cost is $200.
  • $50: Not reasonable, since the minimum cost is $200.
  • $100: Not reasonable, since the minimum cost is $200.
  • $400: Reasonable, as it falls within the expected range of costs (e.g., for 4 days).

Therefore, the only reasonable scale for the vertical axis is:

  • $400
that is a multiple choice question

I apologize for misunderstanding your request! Given that we are dealing with a multiple-choice question regarding reasonable scales for the vertical axis based on the cost function \( t(d) = 50d + 200 \), let's re-evaluate the options provided:

  • $1: Not reasonable (too low).
  • $5: Not reasonable (too low).
  • $25: Not reasonable (too low).
  • $50: Not reasonable (too low).
  • $100: Not reasonable (too low).
  • $400: Reasonable (within the calculated cost for multiple days of rental).

Therefore, the reasonable scale for the vertical axis is:

  • $400

I hope this helps clarify! If you have any more questions or need further assistance, feel free to ask.